What is a multiple What is LCM Find LCM by inspection

Duration: 11 min

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Inside: a video lesson and guided study material.

Module outline

  1. About the course: About the Course
  2. Mathematical Aptitude / गणितीय अभिक्षमता: Number System / संख्या पद्धति, HCF and LCM / महत्तम समापवर्तक और लघुत्तम समापवर्त्य, Divisibility Rules / विभाज्यता के नियम, Percentage / प्रतिशत, Ratio and Proportion / अनुपात और समानुपात, Average / औसत, Profit, Loss and Discount / लाभ, हानि और बट्टा, Time and Work / समय और कार्य, Solid Mensuration / घन क्षेत्रमिति, Simple and Compound Interest / साधारण और चक्रवृद्धि ब्याज, Time, Speed and Distance / समय, चाल और दूरी, Age Problems / आयु संबंधी प्रश्न, Mixture and Alligation / मिश्रण और एलिगेशन, Algebra / बीजगणित, Simplification, Indices and Surds / सरलीकरण, घातांक और करणी, Pipe and Cistern / नल और टंकी, Trigonometry / त्रिकोणमिति, Statistics / सांख्यिकी, Data Interpretation / आँकड़ा निर्वचन, Arithmetic / अंकगणित, Sets, Relations, Functions and Discrete Mathematics / समुच्चय, संबंध, फलन और विविक्त गणित, Number Systems and Number Theory / संख्या पद्धति और संख्या सिद्धांत, Coordinate Geometry, Vectors and 3D Geometry / निर्देशांक ज्यामिति, सदिश और त्रिविमीय ज्यामिति, Polynomials, Equations and Complex Numbers / बहुपद, समीकरण और सम्मिश्र संख्याएँ
  3. Logical Reasoning / तार्किक तर्कशक्ति: Series / श्रेणी, Coding-Decoding / कूट लेखन एवं कूट वाचन, Analogy and Classification / सादृश्यता एवं वर्गीकरण, Blood Relations / रक्त संबंध, Direction and Distance / दिशा एवं दूरी, Order and Ranking / क्रम एवं रैंकिंग, Non-Verbal Reasoning / अशाब्दिक तर्क, Seating Arrangement and Puzzles / बैठक व्यवस्था एवं पहेलियाँ, Syllogisms / न्यायवाक्य, Venn Diagrams, Syllogism and Inequalities / वेन आरेख, न्याय वाक्य एवं असमानता, Mathematical Operations and Missing Numbers / गणितीय संक्रियाएँ एवं लुप्त संख्या, Alphabet and Number Test / वर्णमाला एवं संख्या परीक्षण, Statement-Based Reasoning / कथन आधारित तार्किक विवेचन, Analytical Reasoning (Counting Figures Reasoning) / विश्लेषणात्मक तर्क (आकृति गणना तर्क), Cubes, Dice and Figure Counting / घन, पासा एवं आकृतियों की गिनती, Calendar and Clock / कैलेंडर एवं घड़ी, Clock / घड़ी
  4. General Knowledge / सामान्य ज्ञान: Scientific Achievements and Research / वैज्ञानिक उपलब्धियाँ और अनुसंधान, Chemistry / रसायन विज्ञान, Biology / जीव विज्ञान, History / इतिहास, Geography / भूगोल, Polity / राजव्यवस्था, Indian Economy / भारतीय अर्थव्यवस्था, Current Affairs / समसामयिकी, Static General Knowledge / स्थैतिक सामान्य ज्ञान, State-Specific General Knowledge / राज्य विशेष सामान्य ज्ञान
  5. Art of Teaching / शिक्षण कला: Teaching-Learning Process and Classroom Management / शिक्षण-अधिगम प्रक्रिया एवं कक्षा प्रबंधन, Learners & Learning Process / अधिगमकर्ता और अधिगम प्रक्रिया, Factors Affecting Teaching / शिक्षण को प्रभावित करने वाले कारक, Teaching Methods and Approaches / शिक्षण विधियाँ एवं उपागम, Microteaching and Classroom Communication / सूक्ष्म शिक्षण एवं कक्षा संप्रेषण, Teaching Aids and Educational Technology / शिक्षण सहायक सामग्री एवं शैक्षिक तकनीकी, Assessment and Evaluation / आकलन एवं मूल्यांकन, Teacher: Qualities, Professional Ethics and Development / शिक्षक: गुण, व्यावसायिक नैतिकता एवं विकास, Educational Policies, Acts and Administration / शैक्षिक नीतियाँ, अधिनियम एवं प्रशासन, Curriculum, Arts and Co-curricular Areas / पाठ्यचर्या, कला एवं सह-शैक्षिक क्षेत्र, Guidance and Counselling / निर्देशन एवं परामर्श, Education of Children with Disabilities / दिव्यांग बच्चों की शिक्षा, Micro-Teaching & Teaching Skills / सूक्ष्म शिक्षण और शिक्षण कौशल, Lesson Planning / पाठ योजना
  6. Environmental Science / पर्यावरण विज्ञान: Environment / पर्यावरण
  7. Unit 1 | Digital Electronics: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  8. Unit 2 | COA: Basics of COA, Floating Point Rep, Cache Memory Organization, Input Output Organisation, Instr Formats & Modes, Control Unit Design, Register Transfer and Microoperations, Programming the Basic Computer
  9. Unit 3 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  10. Unit 3 | Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  11. Unit 4 | Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Advanced Algorithms
  12. Unit 5 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management
  13. Unit 6 | Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, SQL, Transaction Management, Concurrency Control
  14. Unit 7 | Computer Networks: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, DLL: Framing, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Net Layer:Routing Protocol, Transport Layer Services, TL: Congestion & UDP, Application Layer
  15. Unit 8 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  16. Unit 9 | Object Oriented Programming: OOPS with C++
  17. Unit 10 | Web Development: HTML Basics, CSS, JavaScript-Basics, XML, Node.js, Git & Github, PHP
  18. Unit 11 | Theory Of Computation: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines
  19. Unit 12 | IoT: Emerging Tech Trends, Cloud Computing, Computer Networks, Internet of Things
  20. Unit 13 | Artificial Intelligence: Approaches to AI, Search Algorithms, Game Playing, Knowledge Representation, Natural Language Processing, Artificial Neural Networks, Genetic Algorithms
  21. Unit 14 | E-Commerce: Electronic Data Interchange and E-Commerce, Role of Internet and Web Services, Security in Mobile and Wireless Computing, Physical Security and Cryptography Basics, Cyber Safety and Security
  22. Unit 15 | Multimedia: Multimedia
  23. Unit 16 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis, DSA using Python
  24. Full Length Mock Tests — General Paper:
  25. Full Length Mock Tests — Computer Science (Paper II):
  26. Full Length Mock Test – General + Computer Science:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video provides a comprehensive lesson on the concepts of Least Common Multiple (LCM) and Highest Common Factor (HCF), presented by an instructor named Yash Jain. The video begins with an introduction to the topic, followed by a clear definition of a 'multiple' as a number that can be divided by another number without a remainder. It then contrasts this with 'factors', explaining that a factor divides a number, while a multiple is divided by a number. The core of the lesson focuses on the method of finding the LCM by inspection, which involves listing the multiples of each number and identifying the smallest common multiple. This method is demonstrated with examples, such as finding the LCM of 5, 7, and 10, which is determined to be 70. The video also introduces the concept of LCM by prime factorization, using the numbers 5, 15, 20, and 30 as an example, where the LCM is found to be 60. The lesson concludes with a key takeaway: the LCM is always greater than or equal to the largest number in the set. The presentation uses a digital whiteboard with handwritten text and diagrams, and includes a small video feed of the instructor.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title card displaying 'LCM & HCF' against a digital background of floating numbers. It then transitions to a classroom setting with a cartoon teacher and a green chalkboard. The instructor, Yash Jain, introduces the topic of 'Least Common Multiple (LCM)' and begins to explain the concept. The on-screen text clearly states 'Least Common Multiple (LCM)' and the instructor's name is visible. The visual style is a mix of animation and a live video feed of the instructor.

  2. 2:00 – 5:00 02:00-05:00

    The video focuses on defining a 'multiple'. The on-screen text asks 'What is a multiple?'. The instructor explains that a multiple of a number is the product of that number and an integer. He provides examples, writing '5 = 5, 10, 15, 20, 25, 30, 35...' and '7 = 7, 14, 21, 28, 35, 42, 49, 56, 63, 70...'. The video then contrasts 'factors' and 'multiples', stating that a 'Factor divides the number' and a 'Multiple is divided by the number'. Examples for the number 12 are used to illustrate this difference, showing its factors {1, 2, 3, 4, 6, 12} and its multiples {12, 24, 36, 48...}. The instructor also notes that factors are always less than or equal to the number, while multiples are greater than or equal to the number.

  3. 5:00 – 10:00 05:00-10:00

    The video explains the method for finding the LCM by inspection. The on-screen text asks 'What is Least Common Multiple (LCM)?'. The instructor demonstrates this by listing the multiples of 5, 7, and 10. He circles the common multiples, such as 70, and identifies the smallest one, concluding that LCM(5, 7, 10) = 70. The video then introduces the second method, 'LCM by Inspection' for the numbers 5, 15, 20, and 30. The instructor lists the multiples of each number, circles the common ones (60, 120, 180...), and identifies the smallest, stating that LCM(5, 15, 20, 30) = 60. A key point is highlighted: 'LCM is always greater than or equal to the largest number'.

  4. 10:00 – 10:43 10:00-10:43

    The video concludes with a final summary slide. The instructor reiterates the key point that the LCM is always greater than or equal to the largest number in the set, with the equation 'LCM ≥ 30' shown for the example of 5, 15, 20, and 30. The video ends with a 'THANKS FOR WATCHING' message on a black background, signaling the end of the lesson.

The video presents a structured and clear lesson on LCM and HCF, starting with foundational definitions and progressing to practical problem-solving methods. It effectively uses visual aids like a digital whiteboard to illustrate concepts such as listing multiples and identifying common values. The core teaching method demonstrated is 'LCM by inspection', which is shown to be a reliable technique for finding the least common multiple of a set of numbers. The lesson is well-organized, moving from basic definitions to worked examples, and concludes with a key takeaway that reinforces the relationship between the LCM and the numbers involved.

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